Method for verifying anti-scrambling efficiency of a communication system

ABSTRACT

A method for the verification of anti-jamming in a communications system comprises several sensors or adaptive antennas, comprising at least the following steps: 
         estimating the mean power π;ˆ y  of the output of the communications system, estimating the respective power values Pu or P′u, of a station u, the antenna noise Pa or P′a, the thermal noise PT, or P′T, 
 
estimating at least one of the following ratios:  
                 J   tot     ⁢     /     ⁢     S   tot       =       (         ∑     p   =   1     P     ;     ;     P   p       )     ⁢     /     ⁢     (         ∑     u   =   1     U     ;     ;     P   u       )                       J   tot     ⁢     /     ⁢     S   u       =       (         ∑     p   =   1     P     ;     ;     P   p       )     ⁢     /     ⁢     P   u                       J   u     ⁢     /     ⁢     S   u       =       (         ∑     p   =   1     P     ;     ;     P   pu       )     ⁢     /     ⁢     P   u                 
comparing at least one of the three ratios with a threshold value.

BACKGROUND OF THE INVENTION

The invention relates to a method to verify the efficiency ofanti-jamming by antenna processing in one or more space communicationson board a geostationary satellite, as well as its implementation fromthe ground.

The invention can be applied in anti-jamming for spacetelecommunications and is a tool of assistance in optimizing theplanning of connection bit rates in a theatre of operations depending onjamming conditions.

At present, anti-jamming by antenna processing is the most efficient wayto protect one or more space or radio communications links againsthostile jamming units. Anti-jamming by antenna processing consists inimplementing what is called an adaptive antenna at reception. The chiefproperty of this adaptive antenna is that it matches its radiationpattern in real time to the received signal, setting pattern holestoward the jamming units while at the same time maintaining sufficientgain in the direction of the link or links to be protected as can beseen in FIG. 1. This result can be obtained from a minimum amount ofinformation on the links to be protected such as knowledge of theposition of the transmitters, the theatre of operations or the learningsequences conveyed by the transmitters without a priori knowledge of thejamming units present. However, in certain cases, the a prioriestimation of the positions of the jamming units may be advantageouslyused by the adaptive antenna so as to simplify the processingoperations.

FIG. 2 shows an adaptive antenna with a purely spatial structure. It isformed by an network of sensors Ci or radiating elements, a set ofdigital or analog reception chains CRi, downstream from the sensors, aset of adaptive filters Fi with one complex coefficient per filter whoserole is to carry out the phase and amplitude weighting of the signalscoming from the difference sensors before summation, and an adaptivealgorithm A whose role is to carry out the real-time matching of thecoefficients of the adaptive filters so as to optimize a criterion as afunction of the information available a priori on the signals ofinterest and therefore the application.

The adaptive antenna can be implemented in an analog, digital or hybridway. In the first case, the weightings are computed and appliedanalogically while, in the second case, they are computed and applieddigitally. In the third case, the set of complex weightings is computeddigitally and copied analogically before summation.

For a digital implantation, the adaptive filters are formed by complexweighting operations whereas, for an analog implantation, these filtersare formed by the cascade connection of a phase-shifter and a variableattenuator or a hybrid quadrature as can be shown in FIG. 3. In thecontext of space communications, when there are no jamming units, theset of weightings synthesizes a coverage (or a spot) on the earth,centered on a given point and having a certain surface area as can beseen in FIG. 4. In general, the coverage is characterized especially bythe 3 dB width of the beam formed by the set of weightings. According tothe size of this 3 dB lobe width or width of the illuminated surfacearea of the earth, we may speak of theatre, regional or global coverage,the latter corresponding to coverage of the entire earth. The workingstations are deployed inside a coverage considered for a given missionand communicate together and/or with the mainland by satellite.

A jamming operation from one or more terrestrial regions jams the usefuluplinks (from the earth to a satellite) and it is the role of theadaptive antenna precisely to carry out anti-jamming on the links bycreating antenna pattern holes toward the jamming units, located outsideor within the coverage and picked up respectively by the minor or majorlobes of the antenna.

SUMMARY OF THE INVENTION

The invention relates to a method for the verification of the efficiencyof the anti-jamming, by adaptive antenna, of the uplink of one or morespace communications links as well as its implementation from theground.

The invention relates to a method of anti-jamming in a communicationssystem comprising several sensors or adaptive antennas. It ischaracterized by the fact that it comprises at least the followingsteps:

-   -   estimating the mean power of the output of the communications        system,    -   estimating the respective power values Pu or P′u, of a station        u, the antenna noise Pa or P′a, the thermal noise PT, or P′T,    -   estimating at least one of the following ratios: $\begin{matrix}        \begin{matrix}        {{J_{tot}\text{/}S_{tot}} = {\left( {{\sum\limits_{p = 1}^{P};};P_{p}} \right)\text{/}\left( {{\sum\limits_{u = 1}^{U};};P_{u}} \right)\quad{with}}} \\        {p = {{the}\quad{jamming}\quad{unit}}} \\        {{= {{sum}\quad{of}\quad{the}\quad{power}\quad{values}\quad{of}\quad{the}\quad{residual}}}\quad} \\        {{{sum}\text{/}{sum}\quad{of}\quad{the}\quad{power}\quad{values}\quad{of}\quad{the}\quad{stations}}\quad} \\        {{on}\quad{the}\quad{reception}\quad{band}\quad{B.}}        \end{matrix} & (22) \\        \begin{matrix}        {{J_{tot}\text{/}S_{u}} = {\left( {{\sum\limits_{p = 1}^{P};};P_{p}} \right)\text{/}P_{u}}} \\        {= {{sum}\quad{of}\quad{the}\quad{power}\quad{values}\quad{of}\quad{the}\quad{residual}}} \\        {{jamming}\quad{units}\text{/}{power}\quad{of}\quad{the}\quad{station}\quad u} \\        {{in}\quad{the}\quad{reception}\quad{band}\quad{B.}}        \end{matrix} & (23) \\        {{J_{u}\text{/}S_{u}} = {\left( {{\sum\limits_{p = 1}^{P};};P_{pu}} \right)\text{/}P_{u}}} & (24)        \end{matrix}$        With Ppu=power of the jamming unit p in the reception band Bu.    -   comparing at least one of the three ratios with a threshold        value.

The invention also relates to a system for the verification ofanti-jamming in a communications system comprising several sensors oradaptive antennas, and a piloting device on the ground. It ischaracterized by the fact that it comprises at least the followingelements: for a verification by channel, from the ground and for areception band B, a computer integrated into the piloting device and anonboard computer, the two computers being programmed to execute thefollowing steps:

-   Communications Channel Power Measurement: Onboard function    parametrized from the ground by the Onboard Param VAA function,-   VAA GAIN: Ground function Sol,-   Communications channel power measurement: onboard function,-   VAA Processing: Ground function.

According to another alternative embodiment, the invention also relatesto a system for the verification of anti-jamming in a communicationssystem comprising several sensors or adaptive antennas, a pilotingdevice on the ground comprising at least the following elements:

For a verification by stations, an onboard computer and a groundcomputer, the computers being programmed to execute the followingfunctions:

-   Communications Channel Power Measurement: onboard function    parametrized from the ground by the Onboard Param VAA function,-   VAA Gain: ground function,-   Acquisition of Communications Channel: onboard function parametrized    from the ground by the function Onboard Param VAA,-   VAA Processing: ground function.

The invention can be applied for example in space communicationssystems.

With the proposed method, it is possible at all times to know whether ornot the anti-jamming applied is effective. If it is not effective, theinformation coming from the method modifies the anti-jammingcharacteristics (choice of the number of type of auxiliary channels inthe case of an OLS (Minor Lobe Opposition) type of processing,alternative parametrization of a pre-synthesis of zeros (PRS) when apiece of a priori information on the position of the jamming units isavailable etc) to increase its efficiency.

BRIEF DESCRIPTION OF THE DRAWINGS

Other features and advantages of the invention shall appear more clearlyfrom the following description given by way of an illustration that inno way restricts the scope of the invention, along with the appendedfigures of which:

FIG. 1 shows a radiation pattern of the antenna after anti-jamming,

FIG. 2 is a functional diagram of a spatial-structure adaptive antenna,

FIG. 3 is a purely spatial adaptive filter for an analog implementation,

FIG. 4 shows the coverage demarcated by the beam associated with the setof weightings when there are no jamming units,

FIG. 5 shows a structure of the adaptive antenna for a digitalimplementation of the filters,

FIG. 6 shows a structure of the adaptive antenna for an analogimplementation of the filters,

FIG. 7 is a functional diagram of the sequencing of the operations forthe implementation of the system for verifying the efficiency of theanti-jamming.

MORE DETAILED DESCRIPTION

The method according to the invention uses especially the information,assumed to be available a priori, on the position and the EquivalentRadiated Isotropic Power (ERIP) sent out by the working stations workingwithin the coverage, also called theatre information. It furthermoremakes use of the characteristics of the active antenna used onboard thesatellite and especially knowledge of the positions and responses of theRE (Radiating Elements) for each direction of space and eachpolarization of the incident field, the set of weightings used for theanti-jamming, the gain and the equivalent noise temperatures of theanalog or a digital reception chains downstream from the sensors and,for an analog or hybrid layout of the set of weightings, that of thedigitization chain if any at output of the antenna.

Before explaining the method according to the invention, a few remindersare given on the signals in a communications system with anti-jamming.

A. Signals at Output of a Communications BFN (Beamforming Network)

It is assumed that each of the N sensors Ci of the network or array ofthe FIG. 2 receives the contribution from U useful sources, coming fromthe theatre of operations, from P jamming units disturbing thecommunications and from a background noise. It is assumed that all thesignals are narrowband signals for the network or array of sensors.

A1. Expression for a Digital Implementation of the Adaptive Antenna

FIG. 5 shows the structure of the adaptive antenna in the case of adigital implementation of the adaptive filters.

The N sensors of the network correspond either to REs, or tosub-networks or sub-arrays preformed in analog mode. In the context of adigital implementation, the vector, x(t), of the envelopes of thesignals brought to the point P1 of the FIG. 5 is written as follows atthe instant t $\begin{matrix}{{{{x(t)} = \sum\limits_{u = 1}^{U}};};{{{s_{u}(t)}S_{u}} + \sum\limits_{p = 1}^{P}};;{{{j_{p}(t)}J_{p}} + {b_{a}(t)} + {b_{T}(t)}}} & (1)\end{matrix}$where b_(a)(t) is the noise vector at the point P1 coming from thenetwork or array of sensors or antennas (external noise+thermal noise ofthe RF reception chains), b_(T)(t) is the thermal noise vector of thedigital chains brought to P1, j_(p)(t) and J_(p) correspond respectivelyto the complex envelope and to the direction vector of the jamming unitp, s_(u)(t) and S_(u) respectively correspond to the complex envelopeand to the direction vector of the station u.

In the general case pertaining to any unspecified sensors, the componentn of the direction vector S_(u) is given byS _(un) =f _(n)(k _(u), η_(u))exp(−jk _(u) r _(u))  (2)where k_(u) and η_(u) are respectively the wave vector and thepolarization parameters of the station u, r_(n) is the position vectorof the sensor n and f_(n)(k_(u), η_(u)) is the complex response of thesensor n in the direction k_(u) for the polarization η_(u).

On the above assumptions, the complex envelope at the instant nT_(e),y(n), of the sampled output of the jamming-protected communications BFNassociated with the set of weighting operations w, is written as follows$\begin{matrix}{{{y(n)}\overset{\Delta}{=}};\quad{{w^{\dagger}G_{num}{x(n)}} = \sum\limits_{u = 1}^{U}};;{{{s_{u}(n)}w^{\dagger}G_{num}S_{u}} + \sum\limits_{p = 1}^{P}};;{{{j_{p}(n)}w^{\dagger}G_{num}J_{p}} + {w^{\dagger}G_{num}{b_{a}(n)}} + {w^{\dagger}G_{num}{b_{T}(n)}}}} & (3)\end{matrix}$where T_(e) is the sampling period, G_(num) is the diagonal matrix (N×N)whose diagonal elements are the gains of the digitization chains.A2. Expression for an Analog or Hybrid Implementation of the AdaptiveAntenna

FIG. 6 shows the structure of the adaptive antenna in the case of ananalog or hybrid implementation of the adaptive antenna, namely for ananalog application of the adapter filters.

The N sensors Ci of the corresponding networks are either REs orsub-networks preformed in analog mode. In the context of an analogimplementation, the vector, x(t), of the envelopes of the signalsbrought to the point P1 of the FIG. 6 is written as follows at theinstant t $\begin{matrix}{{{{x(t)} = \sum\limits_{u = 1}^{U}};};{{{s_{u}(t)}S_{u}} + \sum\limits_{p = 1}^{P}};;{{{j_{p}(t)}J_{p}} + {b_{a}(t)}}} & (4)\end{matrix}$where b_(a)(t) is the noise vector at the point P1 coming from thenetwork of active sensors (external noise+thermal noise of the RFreception chains) and/or the other parameters defined in the aboveparagraph.

On the above assumptions, the complex envelope, y(n), of the sampledoutput of the jamming-protected communications BFN associated with theset of weightings w, is written as follows: $\begin{matrix}{{{y(n)}\overset{\Delta}{=}};{{\alpha\left\{ {{w^{\dagger}{{Gx}(n)}} + {b_{T}(n)}} \right\}} = {\alpha\left\{ {{\sum\limits_{u = 1}^{U};};{{{s_{u}(n)}w^{\dagger}G\quad S_{u}} + \sum\limits_{p = 1}^{P}};;{{{j_{p}(n)}w^{\dagger}G\quad J_{p}} + {w^{\dagger}G\quad{b_{a}(n)}} + {b_{T}(n)}}} \right\}}}} & (5)\end{matrix}$where G is the diagonal matrix (N×N) whose diagonal elements are thegains of the RV chains, w is the vector of the analog weightings, α thegain of the digitization chain of the output of the BFN and b_(T)(n) isthe thermal noise of the digitization chain of the output brought to thepoint P3.

In practice, the matrix G is generally known for a reference temperatureT₀ and is denoted G₀. For an antenna temperature, T_(Ant), the matrix Gis no longer equal to G₀ but takes the valueG=[G ₀ ²+(T _(Ant) −T ₀)δG ² I] ^(1/2)  (6)where δG is a coefficient of variation of the gain in amplitude of theRF chains with the temperature and I is the identity matrix.B. Power of the Output of a Jamming-Protected Communications BFNB1. Expression for a Digital Implementation of the Adaptive Antenna

Assuming that all the signals are decorrelated from one another, fromthe equation (3), we deduce the power of the output of thecommunications BFN in the case of a digital application of the adapterfilters, given by $\begin{matrix}{{{{{{\pi_{y}\overset{\Delta}{=}};} < {E\left\lbrack {\text{|}{y(n)}\text{|}^{2}} \right\rbrack}>={w^{\dagger}G_{num}R_{x}G_{num}^{\dagger}w}} = \sum\limits_{u = 1}^{U}};};{{\pi_{u}\text{|}w^{\dagger}G_{num}S_{u}\text{|}^{2}} + \sum\limits_{p = 1}^{P}};;{{\pi_{p}\text{|}w^{\dagger}G_{num}J_{p}\text{|}^{2}} + {\left( {\eta_{a} + \eta_{T}} \right)w^{\dagger}G_{num}G_{num}^{\dagger}w}}} & (7)\end{matrix}$where <.> corresponds to the operation of temporal averaging on aninfinite horizon of observation, R_(x)=;^(Δ)<E[x(n) x(n)^(†)]> is theaveraged matrix of correlation of x(n), π_(u)=;^(Δ)<E[|s_(u)(n)|²]> isthe mean power of the station u picked up by an omnidirectional RE,π_(p)=;^(Δ)<E[|j_(p)(n)|²]> is the mean power of the jamming unit ppicked up by an omnidirectional RE, η_(a) and η_(T), such that<E[b_(a)(n) b_(a)(n)^(†)]>=η_(a) I and <E[b_(T)(n) b_(T)(n)^(†)]>=η_(T)I, are the equivalent mean power values per sensor brought to the pointP1 in terms of antenna noise and thermal noise respectively, assumed tobe spatially white.

In introducing the power values P_(u), P_(p), P_(a), P_(T), respectivelyof the station u, the jamming unit p, the noise of the antenna a and thethermal noise of the digitization chains at output of the communicationsBFN, respectively defined by:P _(u)=π_(u) |w ^(†) G _(num) S _(u)|²  (8)P _(p)=π_(p) |w ^(†) G _(num) J _(p)|²  (9)P _(a)=η_(a) w ^(†) G _(num) G _(num) ^(†) w  (10)P _(T)=η_(T) w ^(†) G _(num) G _(num) ^(†) w  (11)the expression takes the following form: $\begin{matrix}{{{\pi_{y} = \sum\limits_{u = 1}^{U}};};{P_{u} + \sum\limits_{p = 1}^{P}};;{P_{p} + P_{a} + P_{T}}} & (12)\end{matrix}$

The power values η_(a) and η_(T) are given byη_(a) =kT _(a) B  (13)η_(T) =kT _(T) B  (14)where k is the Boltzman's constant, B is the reception band and T_(a)and T_(T) are the temperatures of the equivalent antenna noise andthermal noise per sensor at P1. The equivalent thermal noise temperatureat P1 per sensor, T_(T), is computed from the ambient temperature,T_(amb), and from the noise factors of the elements of the digitizationchain for the sensor considered. In practice, the equivalent antennanoise temperature at P1 is generally known for a reference temperatureT₀ and is denoted T_(a0). For an antenna temperature, T_(Ant), the noisetemperature T_(a) is no longer equal to T_(a0) but takes the valueT _(a) =T _(a0)+(T _(Ant) −T ₀)δT  (15)where δT is a noise temperature gradient relative to the temperature ofthe antenna, known a priori.

Furthermore, the power π_(u) of the station u is linked to its ERIP,ERIP(u), by the following expressionπ_(u) =ERIP(u)(λ/4πr _(u))²  (16)where λ is the wavelength of the carrier wave, and r_(u) is the distancebetween the station u and the satellite. A similar relation links thepower π_(p) of the jamming unit p and its ERIP, ERIP(p).B2. Expression for an Analog Implementation of the Adaptive Filters

Again assuming signals that are decorrelated from each other, from theexpression (5), we deduce the power of the output of the communicationsBFN in the case of an analog application of the adaptive filtersexpressing $\begin{matrix}{\left. {{{\pi_{y}\overset{\Delta}{=}};} < {E\left\lbrack {\text{|}{y(n)}\text{|}^{2}} \right\rbrack}>=} \middle| \alpha \middle| {}_{2}\left\{ {{w^{\dagger}G\quad R_{x}G^{\dagger}w} + \eta_{T}} \right\} \right. = {\text{|}\alpha\text{|}^{2}\left\{ {{\sum\limits_{u = 1}^{U};};{{\pi_{u}\text{|}w^{\dagger}G\quad S_{u}\text{|}^{2}} + \sum\limits_{p = 1}^{P}};;{{\pi_{p}\text{|}w^{\dagger}G\quad J_{p}\text{|}^{2}} + {\eta_{a}w^{\dagger}G\quad G^{\dagger}w} + \eta_{T}}} \right\}}} & (17)\end{matrix}$where η_(a), such that <E[b_(a)(n) b_(a)(n)^(†)]>=η_(a) I, is the meanpower, at the point P1, of noise per sensor coming from the activenetwork (external noise+thermal noise of the reception chains),η_(T)=;^(Δ)<E[|b_(T)(n)|²]> is the mean power of thermal noise comingfrom the digitization chain brought to P3. The quantities η_(a) andη_(T) are defined respectively by (13) and (14) where T_(a) is theequivalent thermal noise temperature per sensor of the active antenna atP1 and where T_(T) is the equivalent thermal noise temperature comingfrom the digitization chain and brought to P3. Similarly, the powervalues π_(u) and π_(p) are related to the ERIP by the expression (16).

In introducing the power values P′_(u), P′_(p), P′_(a), P′_(T),respectively of the station u, the jamming unit p, the noise of theantenna and the thermal noise of the digitization chain at output of thecommunications BFN defined respectively by:P′ _(u)=|α|²π_(u) |w ^(↑) GS _(u)|²  (18)P′ _(p)=|α|²π_(p) |w ^(↑) GJ _(p)|²  (19)P′ _(a)=|α|²η_(a) w ^(†) GG ^(†) w  (20)P′ _(T)=|α|²η_(T)  (21)the expression (17) takes the form (12).Principle of the Invention

The steps of the method according to the invention rely especially onthe following idea: from an estimation of the mean power, π_(y), theoutput of the communications BFN and the estimates of the quantitiesP_(u), P_(a) et P_(T), P′_(u), P′_(a) and P′_(T), the method makes itpossible to estimate the efficiency of the anti-jamming. This is doneespecially by estimating different residual jamming unit/stationsratios, in the reception band, at output of the communications BFN.

For example, according to an exemplary implementation, the method usesthree residual jamming unit/station ratios whose values make it possibleto evaluate the efficiency of the anti-jamming or of the set ofweightings w considered at output of the communications BFN. The threeratios considered here below in the document correspond to:

-   -   the ratio of the power values respectively of the sum of the        residual jamming units to the sum of the stations in the        reception band B, hereinafter called (J/S per channel) and        referenced J_(tot)/S_(tot)    -   the ratio of the power values respectively of the sum of the        residual jamming units to the power of the station u in the        reception band B, hereinafter called (J/S_(u) per channel) and        referenced J_(tot)/S_(u)    -   the ratio of the power values respectively of the sum of the        residual jamming units to the power of a station, in the band        B_(u) of the station, hereinafter called (J/S_(u) per station or        per link) and referenced, for the station u, J/S_(u).

These quantities are defined respectively by: $\begin{matrix}{{J_{tot}\text{/}S_{tot}} = {\left( {{\sum\limits_{p = 1}^{P};};P_{p}} \right)\text{/}\left( {{\sum\limits_{u = 1}^{U};};P_{u}} \right)}} & (22) \\{{J_{tot}\text{/}S_{u}} = {\left( {{\sum\limits_{p = 1}^{P};};P_{p}} \right)\text{/}P_{u}}} & (23) \\{{J_{u}\text{/}S_{u}} = {\left( {{\sum\limits_{p = 1}^{P};};P_{pu}} \right)\text{/}P_{u}}} & (24)\end{matrix}$where P_(pu) is the power of the jamming unit p in the band B_(u).

The quantity P_(u), P′_(u) respectively defined by (8) or (18), isestimated from a priori knowledge of the theater of operations (ERIP andposition of the working stations), the center frequency of the receptionband, the responses of the sensors of the network, the set of weightingsw well as the gains of the reception and digitization chains, G_(num),G, α, known on an a priori basis or computed by (6) from the temperatureof the antenna and of the parameter δG.

The quantity P_(a), P′_(a) respectively defined by (10) or (20) isestimated from a priori knowledge of the set of weightings w, the gainsof the reception and/or digitization chains, G_(num), G, α, known on ana priori basis or computed by (6) from the temperature of the antennaand the parameter δG (δG is a coefficient of variation of the gain inamplitude of the RF chains with the temperature) as well as from theequivalent noise temperature of the antenna, T_(a), in P1 (itself afunction of the temperature of the antenna, T_(ant)), the referencetemperature T₀, the temperature of the antenna noise, T_(a0) at P1 atthe temperature T₀ and the variation in noise temperature, δT, with thetemperature.

Finally, the quantity P_(T), P′_(T) defined by (11) or (21), isestimated, for a digital implantation, from a priori knowledge of theset of weightings w, gains of the digitization chains, G_(num), as wellas the temperature T_(r) of the equivalent thermal noise per sensor inP1. For an analog implantation of the filters, the quantity P_(T) isestimated from the knowledge of the gain, α, the digitization chain atoutput of the BFN and the thermal noise temperature of this chainbrought to P3, T_(r). In both cases, the quantity T_(r) is estimatedfrom the ambient temperature T_(amb) and from the noise factors of theelements constituting the digitization chain or chains.

C. Estimation of the J/S at Output of the Communications BFN

For a digital implantation of the filters, the estimation of the ratiosdefined by the expressions (22) to (24) necessitates the estimation ofthe quantities π_(y), P_(u), P_(a) and P_(T) defined respectively by(7), (8), (10) and (11) and, for an analog implantation of the filters,it necessitates the estimation of the quantities P′_(u), P′_(a) and P′,defined respectively by (17), (18), (20) and (21).

C1. Estimation of π_(y)

The method estimates the mean power π_(y) of the output of thecommunications BFN from a number K of samples, y(k), 1≦k≦K, of thisoutput. For a sufficient oversampling factor, an asymptotically unbiasedestimator of this mean power is given by: $\begin{matrix}{{{\underset{y}{\overset{\bigwedge}{\pi}};}\overset{\Delta}{=}};{\overset{1}{\overset{\_}{K}}\underset{k = 1}{\overset{K}{;\sum}}};;{\text{|}{y(k)}\text{|}^{2}}} & (25)\end{matrix}$

This estimator becomes consistent for stationary and ergodic outputs andcyclostationary and cycloergodic outputs.

C2. Estimation of P_(u)

The method estimates the values P;ˆ_(u), P;ˆ′_(u) of the power P_(u),P′_(u) defined by (8) or (18) in using firstly the a priori knowledge ofthe parameters w and G_(num) for a digital application of the adaptivefilters and |α|², w and G for an analog application of these filtersand, secondly, the estimation of the parameters π_(u) and S_(u).

The applied set of weightings w is permanently known while the matrixgain G_(num) and scalar gain |α|² of the digitization chains areparameters adjustable from the ground by the operator so as to optimizethe use of the dynamic range of the ADC or ADCs as a function of thejamming environment. The matrix G of the gains in amplitude of theanalog reception chains is mastered, through the expression (6), fromthe knowledge of the matrix G₀ of the gains for the referencetemperature T₀, the parameter δG and the permanent control of thetemperature of the antenna T_(Ant).

The mean power, π_(u), of the station u, received by an omnidirectionalsensor is estimated by the expression (16) where the ERIP, ERIP(u), ofthe station u is known a priori and listed in a mission plan, where λ isdeduced from the frequency channel and where r_(u) is deduced, for ageostationary satellite, from the position of the station u on theearth.

Finally, the direction vector S_(u), whose component n is given by (2),can be deduced from a priori knowledge of the positions, r_(u) of thesensors of the network, of the wave vector k_(u) through the position ofthe station u, the polarization, η_(u) of the station u and the complexresponses f_(n)(k_(u), η_(u)) of the sensors for the wave vector k_(u)and the polarization η_(u).

C3. Estimation of P_(a)

The method estimates the values P;ˆ_(a), P;ˆ′_(a) of the power valuesP_(a), P′_(a) defined by (10) or (20), in using firstly the a prioriknowledge of the parameters w and G_(num) for a digital application ofthe adaptive filters and |α|², w and G for an analog application ofthese filters and, secondly, the estimation of the parameter η_(a).

The mastery of the parameters w, G_(num), G and |α|² is discussed in theprevious paragraph. The estimation of the power, η_(a), of the noise ofthe antenna per sensor at the point P1 is computed by the expression(13) where the equivalent noise temperature of the antenna, T_(a), at P1is obtained by the expression (15) from the a priori knowledge of thereference temperature T₀, the antenna noise temperature, T_(a0), at P1at the temperature T₀, the variation of the noise temperature, δT withthe temperature and the permanent measurement of the temperature of theantenna T_(Ant).

C4. Estimation of P_(T)

The method estimates the values P;ˆ_(T), P;ˆ′_(T) of the power P_(T),P′_(T) defined by (11) or (21), and requires, firstly, a prioriknowledge of the parameters w and G_(num) for a digital application ofthe adaptive filters and |α|² for an analog application of these filtersand, secondly, the estimation of the parameter η_(T).

The control of the parameters w, G_(num) and |α|² is given in theparagraph B. The power, η_(T), is estimated from the expression (14)where T_(T) is the temperature of the equivalent thermal noise of asensor digitization chain brought to P1, for an application of theadaptive filters in digital mode, and of the digitization chain of theoutput of the BFN brought to P3, for an application of the filters inanalog mode. In both cases, the quantity T_(r) is estimated from theambient temperature T_(amb) and from the noise factors of the elementsconstituting the digitization chain or chains.

With the different values π_(y), P_(u), P_(a) and P_(T) having beenestimated, according to the method, at least one of the three ratiosJ;ˆ_(tot)/S;ˆ_(tot), J;ˆ_(tot)/S;ˆ_(u), J;ˆ/S;ˆ_(u) is estimated. Theexpressions have been given for the case of a digital application of theadaptive filters and remain valid in exchanging the letters, P_(u),P_(a) and P_(T), by the letters P′_(u), P′_(a) and P′_(T), for an analogapplication of the adaptive filters.

C5. Estimation of J_(tot)/S_(tot)

From the above estimations, we deduce an estimation,J;ˆ_(tot)/S;ˆ_(tot), of the ratio J_(tot)/S_(tot) defined by (22), givenby $\begin{matrix}{\underset{tot}{\overset{\bigwedge}{J}};{{\text{/}\underset{tot}{\overset{\bigwedge}{S}}}; = {\left( {\underset{y}{\overset{\bigwedge}{\pi}};{- \sum\limits_{u = 1}^{U}};;\underset{u}{\overset{\bigwedge}{P}};{- \underset{a}{\overset{\bigwedge}{P}}};{- \underset{T}{\overset{\bigwedge}{P}}};} \right)\text{/}\left( {{\sum\limits_{u = 1}^{U};};\underset{u}{\overset{\bigwedge}{P}};} \right)}}} & (26)\end{matrix}$C6. Estimation of J_(tot)/S_(u)

From the above estimations, the method deduces an estimation,J;ˆ_(tot)/S;ˆ_(u), of the ratio J_(tot)/S_(u) defined by (23), given by$\begin{matrix}{\underset{tot}{\overset{\bigwedge}{J}};{\text{/}\underset{u}{\overset{\bigwedge}{S}}};{= {\left( {\underset{y}{\overset{\bigwedge}{\pi}};{- \sum\limits_{u = 1}^{U}};;\underset{u}{\overset{\bigwedge}{P}};{- \underset{a}{\overset{\bigwedge}{P}}};{- \underset{T}{\overset{\bigwedge}{P}}};} \right)\text{/}\underset{u}{\overset{\bigwedge}{P}}}};} & (27)\end{matrix}$C7. Estimation of J/S_(u)

The estimation, J;ˆ/S;ˆ_(u), of the ratio J/S_(u) defined by theexpression (24), necessitates the estimation of the total power ofresidual jamming units in the band B_(u) of the working station u. Thisestimation necessitates the following operations:

-   -   reception of the samples, y(k), of the output y(t) of the        communications BFN,    -   bandpass filtering of the samples around the band B_(u). The        samples y_(u)(k) are obtained,    -   estimation of the power of the output filtered by (25) where        y_(u)(k) replaces y(k). We obtain π;ˆ_(yu)    -   estimation of the power values of antenna noise and thermal        noise respectively at output of the BFN in the band B_(u). These        quantities are computed, from the equivalent noise temperatures        computed here above, by the expressions (13) and (14)        respectively, where B is replaced by B_(u). We thus obtain        P;ˆ_(au) and P;ˆ_(Tu),    -   Computation of the power of the stations v other than the        station u in the band B_(u) at output of the communications BFN.        The approach is that of the step B but one in which, for each        station v different from u, the ERIP used in the computation of        π;ˆ_(v) is that of the station v in the band B_(u). Thus the        quantities P;ˆ_(vu) are obtained,    -   computation of the ratio J;ˆ/S;ˆ_(u), by the expression:        $\begin{matrix}        {\overset{\bigwedge}{J};{{\text{/}\underset{u}{\overset{\bigwedge}{S}}}; = {\left( {\underset{yu}{\overset{\bigwedge}{\pi}};{- \underset{u}{\overset{\bigwedge}{P}}};{- \sum\limits_{v \neq u}^{\quad}};;\underset{vu}{\overset{\bigwedge}{P}};{- \underset{au}{\overset{\bigwedge}{P}}};{- \underset{Tu}{\overset{\bigwedge}{P}}};} \right)\text{/}\overset{\bigwedge}{P}}};} & (28)        \end{matrix}$

With the estimate of at least one of the three ratios being known, themethod compares the estimated value or values with a threshold value Vs.

If the value found is above this threshold value then, according to theinvention, a message is sent on the inefficiency of the anti-jamming. Ifnot, the message informs, for example, an operator that the jammingefficiency is sufficient.

The threshold values take account firstly of the permissible jammingpower per station or per channel to carry out the demodulation of thestations and, secondly, the precision of estimation of the previousratios. The computations of precision made in the paragraphs Di showthat, for jamming unit/station ratios at output greater than 0 dB, theprecision of estimation of these ratios by the proposed method is veryhigh whereas this precision decreases with the ratios between thejamming units and the output signal. In this context, it may beconsidered that the anti-jamming is not efficient if the ratios betweenthe jamming units and the output station exceed 0 dB.

Thus, the control of the precision with which the estimators given hereabove estimate the different Jamming unit/Station rations consideredenables especially an efficient operational exploitation of theseestimators. For this reason, the method may comprises a step fordetermining the precision of each of these three estimators.

D1. Precision of Estimation of π_(y)

The estimate π;ˆ_(y) is related to π_(y) by the following expression:π;ˆ_(y)=;^(Δ)π_(y)(1+απ_(y))  (29)where Δπ_(y) characterizes the error on the estimation of Δπ_(y). theprevious expression expressed in dB becomes(π;ˆ_(y))_(dB)=(π_(y))_(dB)+10log₁₀(1+Δπ_(y))=;^(Δ)(π_(y))_(dB)+Δ(π_(y))_(dB)  (30)

Assuming that the samples y(k) are independent (all the sources arespread out in the reception band B), stationary, Gaussian, the estimator(25) is not biased (E[π;ˆ_(y)]=π_(y)) and has a variance:Var[π;ˆ _(y)]=π_(y) /√K  (31)i.e. a mean standard deviation ofσ[π;ˆ_(y)]=π_(y) /√K  (32)

Thus, in 99% of cases, the estimator π;ˆ_(y) is such thatπ_(y)(1−3/√K)≦π;ˆ_(y)≦π_(y)(1+3/√K)  (33)

-   -   where Δπ_(y) is a centered random variable, that is        quasi-Gaussian for K as a great value and having a mean standard        deviation 1/√K. Thus, in 99% of the cases,        −3/√K≦Δπ _(y)≦3/√K  (34)        10log₁₀(1−3/√K)≦Δ(π_(y))_(dB)≦10log₁₀(1+3/√K)  (35)        Digital Application:        For  K = 1000, we  obtain − 0.4  dB ≤ Δ(π_(y))_(dB) ≤ 0.4  dB    i.e.  precision  of ± 0.4  dB.        D2. Precision of Estimation of P_(u)

From the expressions (8), (16) and (18), we deduce the expression of thepower P_(u) at output of the communications BFN for an application ofthe digital and analog filters respectively, given respectively byP _(u) =ERIP(u)(λ/4πr _(u))² |w ^(†) G _(num) S _(u)|²  (36)P′ _(u) =ERIP(u)(λ/4πr _(u))²|α|² |w ^(†) GS _(u)|²  (37)

This means that the power of the station u, P;ˆ_(u) reconstructed fromthe information on the mission, can be written as follows for a digitaland analog application, respectively, of the filtersP;ˆ _(u)=;^(Δ) P _(u)(1+ΔP _(u))=P _(u)(1+ΔERIP(u))(1+Δ|w ^(†) G _(num)S _(u)|²)  (38)P;ˆ′ _(u)=;^(Δ) P′ _(u)(1+ΔP′ _(u))=P′ _(u)(1+ΔERIP(u))(1+Δ|α|²)(1+Δ|w^(†) GS _(u)|²)  (39)where the quantities ΔERIP(u), Δ|α|², Δ|w^(†)G_(num)S_(u)|₂ etΔ|w^(†)GS_(u)|² are the errors in the knowledge, respectively, ofERIP(u), |α|², |w^(†)G_(num)S_(u)|² et |w^(†)GS_(u)|².

From the previous expressions, we deduce that of P;ˆ_(u) in dB, given by(P;ˆ _(u))_(dB)=(P _(u))_(dB)+10log₁₀(1+ΔP _(u))=;^(Δ)(P _(u))_(dB)+Δ(P_(u))_(dB)  (40)where, for an application of the filters in digital modeΔ(P _(u))_(dB)=Δ(ERIP(u))_(dB)+Δ(|w^(†) G _(num) S _(u)|²)_(dB)  (41)whereas, for an application of the filters in analog modeΔ(P′ _(u))_(dB)=Δ(ERIP(^(u)))_(dB)+Δ(|α|²)_(dB)+Δ(|w^(†) GS_(u)|²)_(dB)  (42)

Digital Application:

For example, if it is assumed that

-   -   the uncertainty on the ERIP of the stations, Δ(ERIP(u))_(dB), is        ±2 dB,    -   the uncertainty on the gain of the digitization chain of the        output of the BFN, Δ(|α|²)_(dB), is ±0.5 dB (because of the        drifts in temperature and the effective application of the        gain),    -   the uncertainty, Δ(|w^(†)G_(num)S_(u)|²)_(dB), is ±1 dB because        of ±0.5 dB of uncertainty on the gains of the digitization        chains and ±0.5 dB of uncertainty on the components of the        direction vector S_(u) because of the uncertainties on the        position of the station and on the responses of the sensors,    -   the uncertainty, Δ(|w^(†)G_(num)S_(u)|²)_(dB), is ±1 dB for the        same reasons as above.

The value Δ(P_(u))_(dB)=±3 dB is obtained for a digital application ofthe filters and Δ(P_(u))_(dB)=±3.5 dB for an analog application of thefilters.

D3. Precision of Estimation of P_(a)

From the expressions (10), (13) and (20), we deduce the expression ofthe power P_(a) at output of the communications BFN for an applicationof the digital and analog filters respectively, given respectively by:P _(a) =kT _(a) Bw ^(†) G _(num) G _(num) ^(†) w  (43)P′ _(a) =kT _(a) B|α| ² w ^(†) GG ^(†) w  (44)

This means that the antenna noise power, P;ˆ_(a), reconstructed from theinformation on the reception chains, the set of complex weightings andthe antenna noise temperature can be written as follows for a digitalapplication and an analog application, respectively, of the filters:P;ˆ _(a)=;^(Δ) P _(a)(1+ΔP _(a))=P _(a)(1+ΔT _(a))(1+Δ(w ^(†) G _(num) G_(num) ^(†) w))  (45)P;ˆ′ _(a)=;^(Δ) P′ _(a)(1+ΔP′ _(a))=P′ _(a)(1+ΔT _(a))(1+Δ|α|²)(1+Δ(w^(†) GG ^(†) w))  (46)where the quantities ΔT_(a), Δ|α|², Δ(w^(†)G_(num)G_(num) ^(†)w) etΔ(w^(†)GG^(†)w) are the errors pertaining to the knowledge,respectively, of T_(a), |α|², w^(†)G_(num)G_(num) ^(†)w andw^(†′)GG^(†)w.

From the above expressions, we deduce that of P;ˆ_(a) in dB, given by(P;ˆ _(a))_(dB)=(P _(a))_(dB)+10log₁₀(1+ΔP _(a))=;^(Δ)(P _(a))_(dB)+Δ(P_(a))_(dB)  (47)where, for an application of the filters in digital modeΔ(P _(a))_(dB)=Δ(T _(a))_(dB)+Δ(w ^(†) G _(num) G _(num) ^(†)w)_(dB)  (48)whereas for an application of the filters in analog modeΔ(P′ _(a))_(dB)=Δ(T _(a))_(dB)+Δ(w^(†) GG ^(†)w)_(dB)+Δ(|α|²)_(dB)  (49)

Digital Application:

For example, if it is assumed that:

-   -   the uncertainty on the antenna temperature is ±0.5 dB,    -   the uncertainty on the gain of the digitization chain of the        output of the BFN, Δ(|α|²)_(dB), is ±0.5 dB (because of the        drifts in temperature and the effective application of the        gain),    -   the uncertainties, Δ(w^(†)G_(num)G_(num) ^(†)w)_(dB) and        Δ(w^(†)GG^(†)w)_(dB) are ±0.5 dB because of ±0.5 dB of        uncertainty on the gains of the RF and digitization chains.

Δ(P_(a))_(dB)=±1 dB is obtained for a digital application of the filtersand Δ(P_(u))_(dB)=±1.5 dB for an analog application of the filters.

D4. Precision of Estimation of P_(T)

From the expressions (11), (14) and (21), we deduce the expressions ofthe power P_(T) at output of the communications BFN for an applicationof the digital and analog filters respectively, given respectively byP _(T) =kT _(T) Bw ^(†) G _(num) G _(num) ^(†) w  (50)P′ _(T) =kT _(T) B|α| ²  (51)where T_(T) has a different sense depending on the nature of theimplementation. This means that the antenna noise power, P;ˆ_(T),reconstructed from the information on the reception chains, the set ofcomplex weightings and the thermal noise temperature at P1 for a digitalimplantation and at P3 for an analog implantation is written as followsfor a digital application and an analog application, respectively, ofthe filters:P;ˆ _(T)=;^(Δ) P _(T)(1+ΔP _(T))=P _(T)(1+ΔT _(T))(1+Δ(w ^(†) G _(num) G_(num) ^(†) w))  (52)P;ˆ′ _(T)=;^(Δ) P′ _(T)(1+ΔP′ _(T))=P′ _(T)(1+ΔT _(T))(1+Δ|α|²)  (53)where the quantities ΔT_(T), Δ|α|² and Δ(w^(†)G_(num)G_(num) ^(†)w) arethe errors relating to the knowledge of T_(T), |α|² andw^(†)G_(num)G_(num) ^(†)w respectively.

From the above expressions, we deduce that of P;ˆ_(T) in dB, given by(P;ˆ _(T))_(dB)=(P _(T))_(dB)+10log₁₀(1+ΔP _(T)) ^(Δ) (P _(T))_(dB)+Δ(P_(T))_(dB)  (54)where, for an application of the filters in digital modeΔ(P _(T))_(dB)=Δ(T _(T))_(dB)+Δ(w ^(†) G _(num) G _(num) ^(†)w)_(dB)  (55)whereas, for an application of the filters in analog modeΔ(P′ _(T))_(dB)=Δ(T _(T))_(dB)+Δ(|α|²)_(dB)  (56)

Digital Application:

For example, if it is assumed that:

-   -   the uncertainty on the antenna temperature is ±0.5 dB,    -   the uncertainty on the gain of the digitization chain of the        output of the BFN, Δ(|α|²)_(dB), is ±0.5 dB (because of the        drifts in temperature and the effective application of the        gain),    -   the uncertainties, Δ(w^(†)G_(num)G_(num) ^(†)w)_(dB) are ±0.5 dB        because of ±0.5 dB of uncertainty on the gains of the RF and        digitization chains.

Δ(P_(a))_(dB)=±1 dB is obtained for a digital as well as an analogapplication of the filters.

E. Precision of Estimation of S_(tot)

The estimation, S;ˆ_(tot), de S_(tot) is written as follows:$\begin{matrix}{{{\underset{tot}{\overset{\bigwedge}{S}};}\overset{\Delta}{=}};{{S_{tot}\left( {1 + {\Delta\quad S_{tot}}} \right)} = \sum\limits_{u = 1}^{U}};;{\underset{u}{\overset{\bigwedge}{P}}; = \sum\limits_{u = 1}^{U}};;{{P_{u}\left( {1 + {\Delta\quad P_{u}}} \right)}\quad{giving}\quad{in}\quad{dB}}} & (57) \\{\left( {\underset{tot}{\overset{\bigwedge}{S}};} \right)_{dB} = {\left( S_{tot} \right)_{dB} + {10\quad{\log_{10}\left( {1 + {\Delta\quad S_{tot}}} \right)}}\overset{\Delta}{-}\left( S_{tot} \right)_{dB} + {{\Delta\left( S_{tot} \right)}_{dB}\quad{where}}}} & (58) \\{{\Delta\left( S_{tot} \right)}_{dB} = {10\quad{\log_{10}\left( {{1 +};\frac{{\sum\limits^{U};};{P_{u}\Delta\quad P_{u}}}{{\sum\limits_{u}^{U};};P_{u}};} \right)}}} & (59)\end{matrix}$

Digital Application:

For example, if it is assumed that the precision on the power of thestations is identical for all the stations,Δ(S_(tot))_(dB)≈Δ(P_(u))_(dB)≈±3 dB or ±3.5 dB is obtained according tothe nature of the implantation.

F. Precision of Estimation of J_(tot)

The estimation, J;ˆ_(tot), of J_(tot) is written as follows$\begin{matrix}{{{\underset{tot}{\overset{\bigwedge}{J}};}\overset{\Delta}{=}};{{J_{tot}\left( {1 + {\Delta\quad J_{tot}}} \right)} = \underset{y}{\overset{\bigwedge}{\pi}}};{- \sum\limits_{u = 1}^{U}};;\underset{u}{\overset{\bigwedge}{P}};{- \underset{a}{\overset{\bigwedge}{P}}};{- \underset{T}{\overset{\bigwedge}{P}}};} & (60) \\{\quad{{{{= {{\pi_{y}\left( {1 + {\Delta\quad\pi_{y}}} \right)} - \sum\limits_{u = 1}^{U}}};};\quad{{P_{u}\left( {1 + {\Delta\quad P_{u}}} \right)} - {P_{a}\left( {1 + {\Delta\quad P_{a}}} \right)} - {{P_{T}\left( {1 + {\Delta\quad P_{T}}} \right)}\quad{that}\quad{is}}}},{{in}\quad{dB}}}} & (61) \\{\quad{{\left( {\underset{tot}{\overset{\bigwedge}{J}};} \right)_{dB} = {{\left( J_{tot} \right)_{dB} + {10\quad{\log_{10}\left( {1 + {\Delta\quad J_{tot}}} \right)}}}\overset{\Delta}{=}}};{\left( J_{tot} \right)_{dB} + {\Delta\quad\left( J_{tot} \right)_{dB}\quad{where}}}}} & (62) \\{{\Delta\left( J_{tot} \right)}_{dB} = {10\quad{\log_{10}\left( {1 + {{Error}!}} \right)}}} & (63)\end{matrix}$

From this result, it is deduced that the precision of estimation ofJ_(tot) depends on the relative signal and jamming unit contributions atsampled output of the communications BFN.

More specifically, for jamming residues that are very high before thestations (either because of an absence of anti-jamming or because oflow-performance anti-jamming, when there is high-level jamming at input)it is deduced from (63) that the precision on J_(tot) is close to theprecision on π_(y).

Digital Application:

In these conditions, Δ(J_(tot))_(dB)≈Δ(π_(y))_(dB)≈±0.4 dB.

By contrast, for jamming residues that are very low before the stations(either because of an absence of jamming or because of high-performanceanti-jamming) the total power is close to that of the working stationsand the error may become very great.

G. Precision of Estimation of J_(tot)/S_(u)

The estimation, Est[J_(tot)/S_(u)], of J_(tot)/S_(u) is written asfollows $\begin{matrix}{{{{Est}\left\lbrack {J_{tot}/S_{u}} \right\rbrack}\overset{\Delta}{=}};{{{\left( {J_{tot}/S_{u}} \right)\left( {1 + {\Delta\left( {J_{tot}/S_{u}} \right)}} \right)} = \underset{tot}{\overset{\bigwedge}{J}}};/\underset{u}{\overset{\bigwedge}{S}}};} & \left( {64a} \right) \\{= {{Error}!}} & \left( {64b} \right) \\{whence} & \quad \\{{\left( {1 + {\Delta\left( {J_{tot}/S_{u}} \right)}} \right) = {\left\lbrack {1/\left( {1 + {\Delta\quad P_{u}}} \right)} \right\rbrack\left( {1 + {{Error}!}} \right)\quad{that}\quad{is}}},{{in}\quad{dB}}} & (65) \\{{\Delta\left( {J_{tot}/S_{u}} \right)}_{dB} = {10\quad{\log_{10}\left( {\left\lbrack {1/\left( {1 + {\Delta\quad P_{u}}} \right)} \right\rbrack\left( {1 + {{Error}!}} \right)} \right)}}} & (66)\end{matrix}$

From this result, it is deduced that the precision of estimation ofJ_(tot)/S_(u) depends on the relative signal and jamming unitcontributions at sampled output of the communications BFN.

More specifically, for jamming residues that are very high before thestations (either because of an absence of anti-jamming or because oflow-performance anti-jamming, when there is high-level jamming at input)it is deduced from (66) that the precision on J_(tot)/S_(u) is given by:Δ(J _(tot) /S _(u))_(dB)=10log₁₀((1+Δπ_(y))/(1+ΔP_(u)))=Δ(π_(y))_(dB)−Δ(P _(u))_(dB)  (67)

Digital Application:

In these conditions, Δ(J_(tot)/S_(u))_(dB)≈±3.4 dB.

By contrast, for jamming residues that are very low before the stations(either because of an absence of jamming or because of high-performanceanti-jamming) the total power is close to that of the working stationsand the error may become very great.

H. Precision of Estimation of J_(tot)/S_(tot)

The estimation Est[J_(tot)/S_(tot)], de J_(tot)/S_(tot) can be written$\begin{matrix}{{{{Est}\left\lbrack {J_{tot}/S_{tot}} \right\rbrack}\overset{\Delta}{=}};{{{\left( {J_{tot}/S_{tot}} \right)\left( {1 + {\Delta\left( {J_{tot}/S_{tot}} \right)}} \right)} = \overset{\bigwedge}{\underset{tot}{J}}};/{\underset{u = 1}{\overset{U}{{\sum;};}}\overset{\bigwedge}{\underset{u}{P}}}};} & \left( {67a} \right) \\{= {{{Error}!}\quad{whence}}} & \left( {67b} \right) \\{{\left( {1 + {\Delta\left( {J_{tot}/S_{tot}} \right)}} \right) = {\left\lbrack {{\sum\limits^{U};};{P_{u}/\sum\limits^{U}};;{P_{u}\left( {1 + {\Delta\quad P_{u}}} \right)}} \right\rbrack \times \left( {1 + {{Error}!}} \right)\quad{that}\quad{is}}},\quad{{in}\quad{dB}}} & (68) \\{{\Delta\left( {J_{tot}/S_{tot}} \right)}_{d\quad B} = {{10\quad{\log_{10}\left( \left\lbrack {{\sum\limits^{U};};{P_{u}/\sum\limits^{U}};;{P_{u}\left( {1 + {\Delta\quad P_{u}}} \right)}} \right\rbrack \right)}} + {10\quad{\log_{10}\left( \left( {1 + {{Error}!}} \right) \right)}}}} & (69)\end{matrix}$

From this result, it is deduced that the precision of estimation ofJ_(tot)/S_(tot) depends on the relative signal and jamming unitcontributions at sampled output of the communications BFN.

More specifically, for jamming residues that are very high before thestations (either because of an absence of anti-jamming or because oflow-performance anti-jamming, when there is high-level jamming at input)it is deduced from (69) that the precision on J_(tot)/S_(tot) is givenby $\begin{matrix}{{\Delta\left( {J_{tot}/S_{tot}} \right)}_{dB} = {{10\quad{\log_{10}\left( {\left( {1 + {\Delta\quad\pi_{y}}} \right)\left\lbrack {{\sum\limits^{U};};{P_{u}/\sum\limits^{U}};;{P_{u}\left( {1 + {\Delta\quad P_{u}}} \right)}} \right\rbrack} \right)}} = {{\Delta\left( {\Delta\pi}_{y} \right)}_{dB} + {10\quad{\log_{10}\left( \left\lbrack {{\sum\limits^{U};};{P_{u}/\sum\limits^{U}};;{P_{u}\left( {1 + {\Delta\quad P_{u}}} \right)}} \right\rbrack \right)}}}}} & (70)\end{matrix}$which gives (67) if all the stations have the same precision.

Digital Application:

In these conditions, from the above examples,Δ(J_(tot)/S_(tot))_(dB)≈3.4 dB.

By contrast, for jamming residues that are very low before the stations(either because of an absence of jamming or because of high-performanceanti-jamming) the total power is close to that of the working stationsand the error may become very great.

Exemplary Implementation of the Method in a Communications System

The method whose steps have been explained here above is, for example,used in the system comprising a base located on the ground and includinga computer program to implement the functions described in detail herebelow, the base being linked by means known to those skilled in the artwith one or more satellites equipped with chains such as those describedin FIGS. 5 and 6.

FIG. 7 is a block diagram of an exemplary sequencing of operations. Twocases of operation sequencing are possible depending on whether it issought to estimate the quantities J_(tot)/S_(tot) and J_(tot)/S_(u)relative to the reception band B or, on the contrary, the quantityJ_(u)/S_(u) relative to the band of the station u. In the former case,the term “verification by channel” will be used and in the latter casethe term used will be “verification by station”.

For a verification by channel, the method carries out the operationsdepicted by a solid line in FIG. 7. Starting from the ground and for areception band B, it executes the following functions

-   -   Communications Channel Power Measurement: whose aim is to        estimate the total power available at output of the digitization        chain of the communications BFN for the applied set of weighting        operations and send it to the ground. This function is an        onboard function parametrized from the ground by the function        Onboard Param VAA implemented for example in a computer,    -   VAA GAIN: whose aim is the optimizing, from the results of the        Communications Channel Power Measurement function, of the gain        of the digitization chain of the output of the communications        BFN to be used by the onboard functions. This function is a        ground function,    -   Communications Channel Power Measurement: whose aim is to        estimate and send to the ground the total power available at        output of the digitization chain of the communications BFN for        the applied set of weighting operations and for the gain        optimized earlier,    -   VAA processing: whose aim is to estimate the quantities        J_(tot)/S_(tot) and J_(tot)/S_(u) relative to the reception        band B. This function is a ground function.

For a verification by station, the method carries out the operationsindicated by dashed lines in FIG. 7. From the ground and for a receptionband B, it executes the following functions:

-   -   Communications Channel Power Measurement: whose aim is to        estimate the total power available at output of the digitization        chain of the communications BFN for the applied set of weighting        operations and send it to the ground. This function is an        onboard function parametrized from the ground by the function        Onboard Param VAA function,    -   VAA Gain: whose aim is the optimizing, from the results of the        Communications Channel Power Measurement function, of the gain        of the digitization chain of the output of the communications        BFN to be used by the onboard functions. This function is a        ground function,    -   Communications Channel Acquisition: whose aim is the acquisition        and sending to the ground of the samples available at output of        the digitization chain of the communications BFN for the applied        set of weighting operations and for the previously optimized        gain. This function is an onboard function parametrized from the        ground by the Onboard Param VAA function,    -   VAA processing: whose aim is to estimate the quantities        J_(u)/S_(u) relatives to the stations insert. This function is a        ground function.        Onboard VAA Param Function

Upon reception of the request for verification of the efficiency of theanti-jamming operation, the Onboard VAA Param function is launched. Therole of this function is to prepare the parameters necessary for theCommunications Channel Power Measurement functions or CommunicationsChannel Acquisition functions. These parameters are:

-   -   the identifier of the considered coverage of the satellite,    -   the identifier of the frequency channel of the band B        considered,    -   the gain of the digitization chamber of the output of the        communications BFN to be used by the Communications Channel        Power Measurement functions or Communications Channel        Acquisition functions. Nominally, this gain is settled at its        minimum value,    -   the function to be launched: Communications Channel Power        Measurement functions or Communications Channel Acquisition.        Communications Channel Power Measurement Function:

The Communications Channel Power Measurement function has the followinggoals:

-   -   estimating the available power at output of the digitization        chain of the communications BFN (expression (25)),    -   sending the result of the ground.        Communications Channel Acquisition

The Communications Channel Acquisition function has the following aims:

-   -   acquiring the samples at the output of the communications BFN,    -   sending the samples to the ground.        VAA Gain Function

On the basis of the results of the Communications Channel PowerMeasurement function, the VAA Gain function is aimed at optimizing thegain, G_(x), of the digitization chain of the output of thecommunications BFN so as to exploit the dynamic range of encoding of theADC to the maximum extent without saturating it. More specifically, thisgain is computed from the results of the Communications Channel PowerMeasurement, P_(output), of the initial gain of the reception chains,G_(init), and of the characteristics of the ADC (Gain of the ADCG_(adc), Maximum permissible power at input with the margin of 10 dBtaken into account P_(max)).

If the gain of the digitization chain is considered to be necessarilyincluded between X and Y dB, then the function implements the followingprocessing operations:

-   -   Computation of the power associated with the input of the ADC:        P_(input)=P_(output)/G_(adc),    -   Comparison of P_(input) and P_(max): ΔP=P_(max)−P_(input),    -   Computation of the gain of the digitization chain        -   If ΔP≧0, G_(x)=Inf[G_(init)+ΔP, Y dB]        -   If ΔP<0, G_(x)=Sup[G_(init)+ΔP, X dB]            VAA Processing Function

For the channel verification mode, the VAA Processing Functionimplements the operations described in paragraphs IV.A to IV.F.

For the station verification mode, the VAA Processing Functionimplements the operations described in paragraph IV.G.

1. A method for the verification of anti-jamming in a communicationssystem having several sensors or adaptive antennas, comprising thefollowing steps: estimating a mean power π;ˆ_(y) of the output of thecommunications system, estimating a respective power values Pu or P′u,of a station u, the antenna noise Pa or P′a, the thermal noise PT, orP′T, estimating at least one of the following ratios: $\begin{matrix}\begin{matrix}{{J_{tot}/S_{tot}} = {\left( {{\sum\limits_{p = 1}^{P};};P_{p}} \right)\text{/}\left( {{\sum\limits_{u = 1}^{U};};P_{u}} \right)\quad{with}}} \\\begin{matrix}{p = {{the}\quad{jamming}\quad{unit}}} \\{{= {{sum}\quad{of}\quad{the}\quad{power}\quad{values}\quad{of}\quad{the}\quad{residual}}}\quad} \\{{jamming}\quad{units}\text{/}{sum}\quad{of}\quad{the}\quad{power}\quad{values}} \\{{of}\quad{the}\quad{stations}\quad{on}\quad{the}\quad{reception}\quad{band}\quad{B\left\lbrack \left\lbrack . \right\rbrack \right\rbrack}}\end{matrix}\end{matrix} & \left\lbrack \left\lbrack (22) \right\rbrack \right\rbrack \\\begin{matrix}{{J_{tot}/S_{u}} = {\left( {{\sum\limits_{p = 1}^{P};};P_{p}} \right)\text{/}P_{u}}} \\\begin{matrix}{\quad{= {{sum}\quad{of}\quad{power}\quad{values}\quad{of}\quad{the}}}} \\{{residual}\quad{jamming}\quad{units}\text{/}{power}\quad{of}} \\{{the}\quad{station}\quad u\quad{in}\quad{the}\quad{reception}\quad{band}\quad{B.}}\end{matrix}\end{matrix} & \left\lbrack \left\lbrack (23) \right\rbrack \right\rbrack \\{{J_{u}/S_{u}} = {\left( {{\sum\limits_{p = 1}^{P};};P_{pu}} \right)\text{/}P_{u}}} & \left\lbrack \left\lbrack (24) \right\rbrack \right\rbrack\end{matrix}$ with Ppu=power of the jamming unit p in the reception bandBu. comparing at least one of the three ratios with a threshold value.2. The method for the verification of anti-jamming according to claim 1,comprising a step for estimating the mean power π;ˆ_(y), for an outputfrom a number K of samples, y(k), 1≦k≦K of this output, given by$\begin{matrix}{{{{\overset{\bigwedge}{\pi}}_{y};}\overset{\Delta^{1}}{=}};\overset{\_}{K};{\sum\limits_{k = 1}^{K};};{\text{|}{y(k)}\text{|}^{2}}} & \left\lbrack \left\lbrack (25) \right\rbrack \right\rbrack\end{matrix}$
 3. The method for the verification of anti-jammingaccording to claim 1, comprising a step of estimation P;ˆ_(u), P;ˆ′_(u)of the power P_(u), P′_(u) in using, firstly, a priori knowledge of theparameters w and G_(num) for a digital application of the adaptivefilters and |α|², w and G for an analog application of the filters andsecondly the estimation of the parameters π_(u) and S_(u).
 4. The methodfor the verification of anti-jamming according to claim 1, comprising anestimation P;ˆ_(u), P;ˆ′_(u) of the power P_(u), P′_(u) in using,firstly, a priori knowledge of the parameters w and G_(num) for adigital application of the adaptive filters and |α|², w and G for ananalog application of the filters and secondly the estimation of theparameter η_(a).
 5. The method for the verification of anti-jammingaccording to claim 1, comprising a step of estimation P;ˆ_(u), P;ˆ′_(u)of the power P_(u), P′_(u) in using a priori knowledge of the parametersw and G_(num) for a digital application of the adaptive filters and|α|², w and G for an analog application of the filters and secondly theestimation of the parameter η_(T).
 6. The method for the verification ofanti-jamming according to claim 1 comprising a step of estimationJ;ˆ_(tot)/S;ˆ_(tot), of the ratio J_(tot)/S_(tot) given by$\begin{matrix}{{\overset{\bigwedge}{J}}_{tot};{{\text{/}{\overset{\bigwedge}{S}}_{tot}}; = {\left( {{\overset{\bigwedge}{\pi}}_{y};{- \sum\limits_{u = 1}^{U}};;{\overset{\bigwedge}{P}}_{u};{- {\overset{\bigwedge}{P}}_{a}};{- {\overset{\bigwedge}{P}}_{T}}} \right)\text{/}\left( {{\sum\limits_{u = 1}^{U};};{\overset{\bigwedge}{P}}_{u};} \right)}}} & (26)\end{matrix}$
 7. The method for the verification of anti-jammingaccording to claim 1 and comprising a step of estimationJ;ˆ_(tot)/S;ˆ_(tot), of the ratio J_(tot)/S_(u), given by$\begin{matrix}{{\overset{\bigwedge}{J}}_{tot};{{\text{/}{\overset{\bigwedge}{S}}_{tot}}; = {\left( {{\overset{\bigwedge}{\pi}}_{y};{- \sum\limits_{u = 1}^{U}};;{\overset{\bigwedge}{P}}_{u};{- {\overset{\bigwedge}{P}}_{a}};{- {\overset{\bigwedge}{P}}_{T}}} \right)\text{/}{\overset{\bigwedge}{P}}_{u}}};} & (27)\end{matrix}$
 8. The method of verification of anti-jamming according toclaim 1 comprising a step of estimation J;ˆ/S;ˆ_(u), of the ratioJ/S_(u) in using the total power of residual jamming units in the B_(u)band of the working station u given by $\begin{matrix}{\overset{\bigwedge}{J};{{\text{/}\overset{\bigwedge}{S}}; = {\left( {{\overset{\bigwedge}{\pi}}_{yu};{- {\overset{\bigwedge}{P}}_{u}};{- \sum\limits_{v \neq u}^{\quad}};{\overset{\bigwedge}{P}}_{vu};{- {\overset{\bigwedge}{P}}_{au}};{- {\overset{\bigwedge}{P}}_{Tu}};} \right)\text{/}\overset{\bigwedge}{P}}};} & (28)\end{matrix}$
 9. A method of verification of anti-jamming according toclaim 1 comprising a step of determination of the precision ofestimation, and wherein this value is used to set the threshold.
 10. Asystem for the verification of anti-jamming in a communications systemcomprising several sensors or adaptive antennas, a ground station and apiloting device, comprising at least the following elements: for averification by channel, from the ground and for a reception band B, acomputer integrated into the piloting device and an onboard computer,the two computers being programmed to execute the following steps:Onboard function parameterized from the ground by the Onboard Param Vaafunction, Ground function, onboard function, VAA Processing
 11. A systemfor the verification of anti-jamming in a communications systemcomprising several sensors or adaptive antennas, a ground station and apiloting device, comprising at least the following elements: for averification by station, an onboard computer and a ground computer, thecomputers being programmed to execute the following functions: onboardfunction parameterized from the ground by the Onboard Param Vaafunction, ground function, onboard function parameterized from theground by the Onboard Param Vaa function, ground function.
 12. A use ofthe method according to claim
 1. 13. A use of the system according toclaim 10 for a space communications system.
 14. A use of the systemaccording to claim 11 for a space communications system.